Question

Rewrite y = a(0.25) ¹/⁹ in the form y = a(1+r)' or y = a(1-r). Then state the growth or decay rate.y=The rate is %.This is arate.

Answer 1

INFORMATION:

We have the next function

`y=a(0.25)^{(t)/(9)}`

We must rewrite it in the form y = a(1+r)^t or y = a(1-r)^t and state the growth or decay rate

STEP BY STEP EXPLANATION:

To rewrite the function:

1. Write the original function

`y=a(0.25)^{(t)/(9)}`

2. Use exponential properties

`y=a\lbrack(0.25)^{(1)/(9)}\rbrack^t`

3. Simplify

`y=a(0.86)^t`

4. Rewrite in form y = a(1-r)^t

`y=a(1-0.14)^t`

Finally, r = 0.14. That means that the rate is 14% and since we used the form y = a(1-r)^t, it is a decay rate.

ANSWER:

1.

`y=a(1-0.14)^t`

2. The rate is 14%

3. This is a decay rate.